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We prove a Wiener Tauberian theorem for the L 1 spherical functions on a semisimple Lie group of arbitrary real rank. We also establish a Schwartz-type theorem for complex groups. As a corollary we obtain a Wiener Tauberian type result for compactly supported distributions.

Analogues of the Wiener Tauberian and Schwartz theorems for radial functions on symmetric spaces